Transcript Slide 1

KEY
Methods
1
Applications
1
Methods
2
Applications
2
AQA GCSE Linked Pair Pilot Route Map – Foundation Tier [Year 10]
Year 10
OCTOBER
SEPTEMBER
Wk1
Wk2
Wk3
Wk4
Indices
and
Powers
Number
Number
NOVEMBER
Wk11
Wk6
Fractions ,
Decimals and
Percentages
Wk13
Wk14
Ratio and
Proportion
Ratio and
Proportion
JANUARY
Fractions,
Decimals and
Percentages
Wk22
Equations, Graphs and
Formulae
Wk15
Algebraic
Argument
Wk16
Wk23
Equations,
Formulae and
Inequalities
Wk24
Holiday
Wk32
Wk25
Holiday
Basic Algebra
Wk18
Holiday
Wk19
January
Examinations
Wk33
Wk34
Scatter
Graphs
Coordinates and Graphs
Wk26
Wk27
Wk28
Wk29
Statistical
Measures
Probability
Representing Data
Wk30
Probability
Wk35
Wk36
JUNE
Wk37
Wk38
Wk39
Wk40
Holiday
Finance
Revision
JULY
June
Examinations
Wk20
March
Examinations
Holiday
Wk42
Wk10
November
Examinations
MAY
JUNE
June
Examinations
Wk9
MARCH
Collecting data
Wk41
Wk17
Holiday
APRIL
Wk31
Wk8
JANUARY
FEBRUARY
Wk21
Holiday
Wk7
DECEMBER
Wk12
Basic
Algebra
Wk5
NOVEMBER
Wk43
Number
Wk44
Wk45
Multiples,
Factors and
Primes
Year 11
AQA GCSE Linked Pair Pilot Route Map – Foundation Tier [Year 11]
Year 11
OCTOBER
SEPTEMBER
Wk1
Wk2
Venn
Diagrams
Wk3
Wk4
Wk5
Angles
Sequences
NOVEMBER
Wk13
Wk14
Equations
Polygons and
Circles
Wk22
Wk15
Wk16
Perimeter, Area
and Volume
Wk23
Trial and
Improvement
Wk31
Wk32
Linear and
Real Life
Graphs
Wk24
Wk25
June
Examinations
Year 10
Number
Wk27
March
Examinations
Perimeter,
Area and
Volume
Wk28
Percentage,
Ratio and
Proportion
Wk29
Wk34
Angles Bearings
Wk35
Polygons
and Circles
Wk43
Wk44
Wk45
Wk36
Coordinates
and Graphs
Wk30
Holiday
Equations
MAY
Wk33
Wk20
January
Examinations
Holiday
Wk26
Pythagoras
JULY
Wk42
Wk19
MARCH
Measures
JUNE
June
Examinations
Wk18
Coordinates
APRIL
Wk41
Wk17
Pythagoras
Holiday
Approximation
and
Calculators
Wk10
November
Examinations
Transformations
FEBRUARY
Wk21
Wk9
JANUARY
Holiday
JANUARY
Holiday
Wk8
DECEMBER
Wk12
Shapes
Wk7
Holiday
Algebraic
Manipulation
Wk11
Wk6
NOVEMBER
JUNE
Wk37
Wk38
Wk39
Holiday
Shapes
Transformations
Wk40
Loci and
Construction
Unit M1 – Number (Slide 1 of 3)
Candidates should be able to:
Continued
on next
page
Teachers own notes
 Understand and use number operations and
the relationship between them, including inverse
operations and hierarchy of operations.
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Unit M1 – Number (Slide 2 of 3)
Candidates should be able to:
Continued
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Teachers own notes
Arithmetic of real numbers:
add, subtract, multiply and divide any number
Non-calculator arithmetic competency will be
assessed in this unit.
Calculations will be restricted to 3 digit integers
and decimals up to two decimal places.
Multiplication will be limited to 3- digit integers
by 2-digit integers.
 For non-calculator work multiplication and
division of decimals will be limited to multiplying
or dividing by a single digit integer or decimal
number to 1 significant figure.
Addition and subtraction of fractions without a
calculator will be assessed.
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Unit M1 – Number (Slide 3 of 3)
Candidates should be able to:
Teachers own notes
Use the concepts and vocabulary of factor
(divisor) multiple and prime numbers.
These terms will not be explicitly assessed in this
unit but their meaning should be known as they
could be used in a question on number, algebra or
probability. These terms could appear in any
section. The explicit testing of these terms will be
in M2.
Use calculators effectively and efficiently
(Calculators are only allowed in Section A).
Candidates should know not to round off values
during the intermediate steps of a calculation.
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Unit M1 – Indices and Powers
Candidates should be able to:
Numbers and their representations including
powers, roots, indices (integers).
Knowledge of powers, roots and indices will be
assessed in Section B (non calculator) although
they can occur in number, algebra and probability
questions in Section A.
Candidates should also understand that an
integer is a positive or negative whole number
and would, for example, if describing the integer
members of two overlapping inequalities or sets,
include zero.
Candidates should know the squares and
corresponding roots up to 15  15 and the cubes
and corresponding roots of the cubes of 1, 2, 3, 4,
5 and 10.
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Unit A1 – Number (Slide 1 of 2)
Continued
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page
Candidates should be able to:
Teachers own notes
Understand and use number operations and
the relationship between them, including inverse
operations and hierarchy of operations.
Understand numbers and their representation
including powers, roots, indices (integer values).
Where powers, indices and roots occur in this
unit it will be in the context of problems in
number, finance, algebra or statistics. Candidates
will be expected to use a calculator to calculate
powers and roots.
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Unit A1 – Number (Slide 2 of 2)
Candidates should be able to:
Teachers own notes
Use calculators effectively and efficiently,
including statistical functions.
Candidates should be able to use a calculator
for: calculations involving the four rules; to check
answers; enter complex calculations such as
estimating the mean of a grouped frequency
table; calculations using the four rules with
fractions; calculations using the functions x 2, x 3,
x n, √x, 3 √x, 1/x. The term reciprocal need not be
known at Foundation tier.
Candidates should be able to interpret the
calculator display (for example, values that have
been rounded) and understand that 3.6 as a
money answer should be written as £ 3.60
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Unit M1 – Fractions, Decimals and Percentages
Candidates should be able to:
Understand that ‘percentage’ means ‘number
of parts per 100’ and use this to compare
proportions.
In Section B (non calculator) questions will be
based on a starting point of calculating 50%, 25%,
10% or 1%.
Use multipliers for percentage change.
In Section B (non calculator) percentage change
will be based on a starting point of 50%, 25%,
10% or 1%. Use of a multiplier will give a decimal
product. Calculating the percentage change and
adding or subtracting may be a more efficient
method.
Interpret fractions, decimals and percentages as
operators.
Understand and use the relationship between
ratio, fractions and decimal representations.
Candidates should know how to convert a
fraction to a decimal.
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Unit A1 – Fractions, Decimals and
Percentages (Slide 1 of 2)
Candidates should be able to:
Continued
on next
page
Teachers own notes
Understand that ‘percentage’ means ‘number
of parts per 100’ and use this to compare
proportions.
Percentage questions will not be assessed
explicitly in this unit but questions may involve a
comparison using percentages.
Use multipliers for percentage change.
This reference will be assessed in this unit in
the context of finance or statistics.
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Unit A1 – Fractions, Decimals and
Percentages (Slide 2 of 2)
Candidates should be able to:
Teachers own notes
Interpret fractions, decimals and percentages
as operators.
Candidates should be able to: use percentages
to interpret or compare statistical diagrams or
data sets; interpret a percentage as a multiplier
when solving problems.
Candidates should be able to convert between
fractions, decimals and percentages to find the
most appropriate method of calculation.
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Unit M1 – Basic Algebra
Candidates should be able to:
Distinguish the different roles played by letter
symbols in Algebra, using the correct notation.
Distinguish in meaning between the words
equation, inequality, formula and expression.
Manipulate algebraic expressions by collecting
like terms, by multiplying a single term over a
bracket, taking out common factors.
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Unit A1 – Basic Algebra
Candidates should be able to:
Manipulate algebraic expressions by collecting
like terms, by multiplying a single term over a
bracket, taking out common factors.
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Teachers own notes
Unit M1 – Ratio and Proportion
Candidates should be able to:
Understand and use the relationship between
ratio, fractions and decimal representations.
Candidates should know how to convert a
fraction to a decimal.
Understand and use direct proportion.
Divide a quantity in a given ratio.
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Unit A1 – Ratio and Proportion
Candidates should be able to:
Understand and use direct proportion.
Divide a quantity in a given ratio.
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Unit M1 – Algebraic Argument
Candidates should be able to:
Use algebra to support and construct
arguments.
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Unit M1 – Coordinates and Graphs
Candidates should be able to:
Use the conventions for coordinates in the
plane and plot points in all four quadrants.
In this unit plotting points will be used when
drawing straight line graphs
Recognise and plot equations that correspond
to straight-line graphs in the coordinate plane.
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Unit A1 – Scatter Graphs
Candidates should be able to:
Recognise correlation and draw and/or use lines
of best fit by eye, understanding and interpreting
what these represent, and appreciating that
correlation does not imply causality.
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Unit M1 – Equations, Graphs and Formulae
Candidates should be able to:
Set up, and solve simple equations and
inequalities.
Solve quadratic equations approximately using
a graph.
Derive a formula, substitute numbers into a
formula and change the subject of a formula.
Candidates should be able to: use formulae from
mathematics; use formulae expressed in words
and symbols; substitute numbers into a formula;
change the subject of a formula which will involve
at most two letters and two inverse operations to
rearrange and will not include any terms
containing a power.
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Unit A1 – Equations, Formulae and Inequalities
Candidates should be able to:
Set up, and solve simple equations and
inequalities.
Derive a formula, substitute numbers into a
formula.
In this unit the formulae will be derived from
practical situations such as the time taken to cook
a turkey or how much to charge for a taxi journey.
Solve linear inequalities in one variable, and
represent the solution set on a number line.
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Unit A1 – Statistical Measures
Candidates should be able to:
Calculate, median, mean, range and modal
class.
Discuss and start to estimate risk.
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Unit A1 – Representing Data (Slide 1 of 2)
Candidates should be able to:
Continued
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Teachers own notes
Design, use and interpret two-way tables for
discrete and grouped data.
Look at data to find patterns and exceptions.
Compare distributions and make inferences.
Produce and interpret charts and diagrams for
categorical data including bar charts, pie charts
and pictograms.
Produce and interpret diagrams for grouped
and ungrouped data, including tally charts,
vertical line graphs, Stem-and-leaf diagrams,
frequency polygons and histograms with equal
class intervals.
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Unit A1 – Representing Data (Slide 2 of 2)
Candidates should be able to:
Teachers own notes
Work with time series including their graphical
representation.
Understand that a time series is a series of data
points typically spaced over uniform time intervals.
Plot and interpret time-series graphs.
Be able to use a time series graph to predict a
subsequent value.
Understand that if data points are joined with a
line then the line will not represent actual values
but will show a trend.
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Unit M1 – Probability (Slide 1 of 3)
Candidates should be able to:
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Teachers own notes
Understand and use the vocabulary of
probability and the probability scale.
Candidates should be able to: use words to
indicate the chances of an outcome for an event;
use fractions, decimals or percentages to put
values to probabilities; place events with equally
likely outcomes on a probability scale from 0 to 1.
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Unit M1 – Probability (Slide 2 of 3)
Candidates should be able to:
Continued
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Teachers own notes
Use Venn diagrams to represent the number of
possibilities and hence find probabilities.
Understand that P(A) means the probability of
event A
Understand that P(A’) means the probability of
not event A
Understand that P(A  B) means the probability
of event A or B
Understand that P(A  B) means the probability
of event A and B.
Compare experimental data and theoretical
probabilities, and make informal inferences about
the validity of the model giving rise to the
theoretical probabilities.
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Unit M1 – Probability (Slide 3 of 3)
Candidates should be able to:
Teachers own notes
Understand that when a statistical experiment
or survey is repeated there will usually be
different outcomes, and that increasing sample
size generally leads to better estimates of
probability and population characteristics.
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Unit A1 – Probability (Slide 1 of 2)
Candidates should be able to:
Continued
on next
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Teachers own notes
Understand and use the vocabulary of
probability and the probability scale.
In this unit, probability questions will be about
applying probability theory to statistical problems.
Understand and use theoretical models for
probabilities including the model of equally likely
outcomes.
In this unit this reference will only be assessed
alongside reference A1.S3, comparing a relative
frequency with a theoretical frequency.
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Unit A1 – Probability (Slide 2 of 2)
Candidates should be able to:
Teachers own notes
Understand and use estimates of probability
from relative frequency.
Candidates should be able to estimate
probabilities by considering relative frequency.
Questions in this unit will be set in a realistic
context.
Understand that when a statistical experiment
or survey is repeated there will usually be
different outcomes, and that increasing sample
size generally leads to better estimates of
probability and population characteristics.
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Unit A1 – Collecting Data
Candidates should be able to:
Data Handling Cycle.
Design an experiment or survey, identifying
possible sources of bias.
Design data-collection sheets distinguishing
between different types of data.
Extract data from publications, charts, tables
and lists.
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Unit A1 – Finance (Slide 1 of 5)
Candidates should be able to:
Continued
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Teachers own notes
Carry out calculations relating to enterprise,
saving and borrowing, appreciation and
depreciation.
Understand and calculate VAT.
Understand basic business terms such as profit
and loss and carry out related calculations.
Understand how interest is calculated and
related terms such as principal, interest rate, per
annum and be able to calculate simple interest.
Understand terms related to income tax such as
personal allowance, taxable income and tax bands
and carry out related calculations.
Understand that the value of items such as cars,
for example, will depreciate (or appreciate) over
time and carry out related calculations.
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Unit A1 – Finance (Slide 2 of 5)
Candidates should be able to:
Continued
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Use mathematics in the context of personal and
domestic finance including loan repayments,
budgeting, RPI and CPI , exchange rates and
commissions.
Understand and calculate wages and salaries
given hourly/weekly/monthly rates of pay.
Understand the terms gross wage/salary and net
wage/salary and that wages and salaries are
subject to Tax and National insurance.
Understand terms such as bonus and sales
commission.
Understand that overtime is often paid at a
higher rate and should understand terms such as
‘time and a half’ and carry out related calculations.
[CONTINUED ON NEXT SLIDE]
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Unit A1 – Finance (Slide 3 of 5)
Candidates should be able to:
Continued
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Understand the term ‘Retail Price Index’ (RPI)
and be able to do related calculations.
Understand the term ‘Consumer Price Index’
(CPI) and be able to do related calculations.
Understand that different currencies have a
variable exchange rate and carry out related
calculations.
Understand that when exchanging money or
carrying out a financial transaction that a
commission may be charged.
Know that loans are normally paid back at a fixed
rate over a fixed number of months and that the
amount paid back will vary depending on the
number of months taken to pay the loan back.
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Unit A1 – Finance (Slide 4 of 5)
Candidates should be able to:
Continued
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Teachers own notes
Use spreadsheets to model financial, statistical
and other numerical situations.
Candidates should be able to:
Read a spreadsheet and be able to pick out
information.
Understand and construct formulae, using
normal spreadsheet notation
(see notes below).
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Unit A1 – Finance (Slide 5 of 5)
Candidates should be able to:
Teachers own notes
Construct and use flow charts.
Candidates should be able to:
Understand the symbols used in flow charts (see
notes below).
Work through a flow chart to obtain the final
output.
Construct a simple flow diagram to perform a
simple financial or mathematical calculation which
may involve a repeated action.
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Unit M2 – Number (Slide 1 of 3)
Candidates should be able to:
Continued
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page
Teachers own notes
Understand and use number operations and the
relationship between them, including inverse
operations and hierarchy of operations.
Add, subtract, multiply and divide any number.
The four rules will be assessed in the context of
problems in number, algebra and geometry.
Candidates will be expected to use a calculator.
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Unit M2 – Number (Slide 2 of 3)
Candidates should be able to:
Continued
on next
page
Teachers own notes
Understand numbers and their representation
including powers, roots, indices (integers).
Powers and roots will not be assessed in this units
but knowledge of square, cube, square root and
cube root will be needed for questions involving
area and volume.
Candidates will be expected to use a calculator to
calculate powers and roots.
Approximate to specified degrees of accuracy
including a given power of ten, number of
decimal places and significant figures.
Candidates should be able to round to;
The nearest 10, 100 or 1000
1, 2 or 3 decimal places
1 significant figure.
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Unit M2 – Number (Slide 3 of 3)
Candidates should be able to:
Teachers own notes
Understand that ‘percentage’ means ‘number of
parts per 100’ and use this to compare
proportions.
Questions explicitly assessing knowledge of
percentage will be assessed in this unit and in M1.
Understand and use the relationship between
ratio and fractions.
Find proportional change, using fractions,
decimals and percentages.
Use calculators effectively and efficiently.
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Unit M2 – Multiples, Factors and Primes
Candidates should be able to:
Use the concepts and vocabulary of factor
(divisor) multiple, common factor, common
multiple, highest common factor, least common
multiple, prime numbers and prime factor
decomposition.
Understand that factors of a number can be
derived from its prime factorisation.
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Unit M2 – Venn Diagrams
Candidates should be able to:
Understand and use Venn diagrams to solve
problems.
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Unit M2 – Algebraic Manipulation
Candidates should be able to:
Distinguish the different roles played by letter
symbols in Algebra, using the correct notation.
Manipulate algebraic expressions by collecting
like terms, by multiplying a single term over a
bracket, taking out common factors.
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Teachers own notes
Unit M2 – Angles
Candidates should be able to:
Recall and use properties of angles at a point on
a straight line (including right angles),
perpendicular lines and vertically opposite angles.
Understand and use the angle properties of
parallel and intersecting lines, triangles and
quadrilaterals.
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Unit M2 – Sequences
Candidates should be able to:
Generate terms of a sequence using term-toterm and position-to-term definitions
Form linear expressions to describe the nth
term of a sequence.
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Unit M2 – Equations
Candidates should be able to:
Set up, and solve simple equations.
Recognise and use equivalence in numerical,
algebraic and graphical representations.
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Unit M2 – Transformations
Candidates should be able to:
Describe and transform 2D shapes using single
or combined rotations, reflections, translations or
enlargements by a positive scale factor and
distinguish properties that are preserved under
particular transformations.
Use 2D vectors to describe translations.
Understand congruence and similarity, including
the relationship between lengths, in similar
figures.
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Unit M2 – Shapes
Candidates should be able to:
Recall the properties and definitions of special
types of quadrilateral, including square, rectangle,
parallelogram, trapezium, kite and rhombus.
Recognise reflection and rotational symmetry of
2D shapes.
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Unit M2 – Polygons and Circles
Candidates should be able to:
Calculate and use the sums of the interior and
exterior angles of polygons.
Solve problems in the context of tiling patterns
and tessellation.
Understand that a tessellation of shapes covers
the plane with no gaps.
Understand that shapes that fit together at a
point in a tessellation have an angle sum of 360°.
Distinguish between centre, radius, chord,
diameter, circumference, tangent, arc, sector and
segment.
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Unit M2 – Perimeter, Area and Volume
Candidates should be able to:
Find circumferences of circles and areas
enclosed by circles.
Calculate perimeters and areas of shapes made
from triangles and rectangles.
Calculate volumes of right prisms and of shapes
made from cubes and cuboids.
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Unit M2 – Pythagoras
Candidates should be able to:
Use Pythagoras’ theorem in 2D.
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Unit M2 – Coordinates
Candidates should be able to:
Use the conventions for coordinates in the
plane and plot points in all four quadrants.
Use geometric information to complete
diagrams on a coordinate grid.
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Unit A2 - Number
Candidates should be able to:
Understand and use number operations and
the relationship between them, including inverse
operations and hierarchy of operations.
Use the concepts and vocabulary of factor
(divisor) multiple, common factor, common
multiple and prime number.
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Teachers own notes
Unit A2 – Approximation and Calculators
Candidates should be able to:
Approximate to specified degrees of accuracy
including a given power of ten, number of
decimal places and significant figures.
Candidates should be able to round to;
The nearest 10, 100 or 1000
1, 2 or 3 decimal places
1 significant figure.
Use calculators effectively and efficiently.
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Unit A2 – Trial and Improvement
Candidates should be able to:
Find approximate solutions of equations using
systematic trial and improvement.
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Unit A2 – Measures
Candidates should be able to:
Interpret scales on a range of measuring
instruments and recognise the inaccuracy of
measurements.
Convert measurements from one unit to
another.
Make sensible estimates of a range of
measures.
Understand and use compound measures in
familiar and unfamiliar contexts.
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Unit A2 – Pythagoras’s Theorem
Candidates should be able to:
Use Pythagoras’ theorem in 2D.
Candidates should understand, use and recall
Pythagoras’ theorem. In this unit this will be
assessed in the context of a geometrical problem.
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Unit A2 – Perimeter, Area and Volume
Candidates should be able to:
Calculate perimeters and areas of shapes made
from triangles and rectangles.
Calculate volumes of right prisms and of shapes
made from cubes and cuboids.
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Unit A2 – Percentage, Ratio and Proportion
Candidates should be able to:
Understand that ‘percentage’ means ‘number
of parts per 100’ and use this to compare
proportions.
Percentage questions will not be assessed
explicitly in this unit but questions may involve a
comparison using percentages.
Find proportional change.
Divide a quantity in a given ratio.
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Unit A2 – Equations
Candidates should be able to:
Set up, and solve simple equations.
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Teachers own notes
Unit A2 – Linear and Real Life Graphs
Candidates should be able to:
Find and interpret gradients of straight line
graphs in practical contexts.
Construct linear functions from real-life
problems and plot their corresponding graphs.
Recognise and use graphs that illustrate direct
proportion.
Discuss, plot and interpret graphs (which may
be non-linear) modelling real situations,
including journeys/travel graphs.
Calculate areas under graphs consisting only of
straight lines and interpret the result.
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Unit A2 – Angles
Candidates should be able to:
Measure and draw lines and angles.
Recall and use properties of angles at a point
on a straight line (including right angles),
perpendicular lines and vertically opposite
angles.
Understand and use the angle properties of
parallel and intersecting lines, triangles and
quadrilaterals.
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Unit A2 – Bearings
Candidates should be able to:
Understand and use bearings.
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Unit A2 – Polygons and Circles
Candidates should be able to:
Distinguish between centre, radius, chord,
diameter, circumference, tangent, arc, sector and
segment.
Find circumferences of circles and areas
enclosed by circles.
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Unit A2 – Coordinates and Graphs
Candidates should be able to:
Use the conventions for coordinates in the
plane and plot points in all four quadrants.
In this unit plotting points will be used when
constructing linear functions from real-life
graphs.
Recognise and plot equations that correspond
to straight-line graphs in the coordinate plane.
In this unit the straight lines graphs will be from
practical situations such as a conversion graphs.
Find approximate solutions of equations using
graphical methods.
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Unit A2 – Shapes
Candidates should be able to:
Recall the properties and definitions of special
types of quadrilateral, including square,
rectangle, parallelogram, trapezium, kite and
rhombus.
Recognise reflection and rotational symmetry
of 2D shapes.
Use 2D representations of 3D shapes.
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Unit A2 – Transformations
Candidates should be able to:
Understand congruence and similarity,
including the relationship between lengths, in
similar figures.
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Unit A2 – Loci and Constructions
Candidates should be able to:
Use and interpret maps and scale drawings.
Draw triangles and other 2D shapes using a
ruler, pair of compasses and protractor.
Use straight edge and a pair of compasses to
do constructions.
Construct loci.
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